Hausdorff Fractal Derivative Model to Characterize Transport of Inorganic Arsenic in Porous Media

The increasing severity of arsenic pollution has progressively threatened human life and attracted much attention. One of the important topics in environmental sciences is to accurately describe the inorganic arsenic transport in heterogeneous porous media, occurring anomalous diffusion phenomenon, which ultimately benefits the control of arsenic pollution. In this paper, we re-evaluate the dataset of the inorganic arsenic transport in porous media in previous work by using a time-Hausdorff fractal model (HADE). Transport experiments of arsenic-carrying (As(V)) ferric humate complex colloids through a quartz sand column were carried out under varying dissolved organic matter (humic acid) concentrations, pH values, ionic strengths, and ferric concentrations. The results show that under our experimental settings, arsenic migration is promoted with the increase of concentrations of HA, ferric ion and sodium ion, and pH to varying degrees. The intensity of arsenic sub-diffusion behavior is opposite to that of arsenic transport. The HADE model can describe the migration behavior of arsenic well, and the value of the time fractal derivative can reflect the diffusion intensity of arsenic migration to a certain extent. By comparing the HADE model, ADE model, and time-fractional model (fADE) to the experimental data, the HADE model can significantly improve all the simulation results of capturing As(V) breakthrough curves (BTCs).